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The Porous Medium EquationMathematical Theory$
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Juan Luis Vazquez

Print publication date: 2006

Print ISBN-13: 9780198569039

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198569039.001.0001

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THE CAUCHY PROBLEM. L 1-THEORY

THE CAUCHY PROBLEM. L 1-THEORY

Chapter:
(p.194) 9 THE CAUCHY PROBLEM. L 1-THEORY
Source:
The Porous Medium Equation
Author(s):

Juan Luis Vázquez

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198569039.003.0009

This chapter examines the Cauchy problem, or pure initial value problem, for the PME and the GPME in d-dimensional space, d = 1. It concentrates the main effort on the PME with zero forcing term. It considers solutions which are integrable with respect to the space variables, so-called solutions with finite mass, and develops the corresponding L 1 theory. It establishes well-posedness for the Cauchy problem in this setting, which is the one most often found in relevant literature and applications.

Keywords:   Cauchy problem, pure initial value problem, PME, GPME, solutions with finite mass, L1

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